NIK and RRPlots

The libraries

library(survival)
library(FRESA.CAD)
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library(Biobase)
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op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)
if (!require("BiocManager", quietly = TRUE))
{
    install.packages("BiocManager")
    BiocManager::install("seventyGeneData")
}
## Bioconductor version '3.15' is out-of-date; the current release version '3.17'
##   is available with R version '4.3'; see https://bioconductor.org/install
library(seventyGeneData)
data(vanDeVijver)
class(vanDeVijver)
## [1] "ExpressionSet"
## attr(,"package")
## [1] "Biobase"

Getting the clinical data

pdata <- pData(vanDeVijver)

ROC Plots

table(pdata$Posnodes)

n y 151 144

pander::pander(table(pdata$TTMevent))
0 1
194 101 
pmroc <- plotModels.ROC(cbind(pdata$TTMevent,-pdata$C1used),name="NIK",thr= -0.4) ## Using paper threshold

par(op)

RR Plot Signature correlation

rdata <- cbind(pdata$TTMevent,pdata$C1used)


RRAnalysisCI <- RRPlot(rdata,atRate=c(0.10,0.05),
                     timetoEvent=pdata$RFS,
                     title="Signature: Breast Cancer",
                     ysurvlim=c(0.00,1.0))

par(op)

CI Performance all data

pander::pander(t(RRAnalysisCI$keyPoints),caption="Threshold values")
Threshold values
  @:0.1 @:0.05 @MAX_BACC @MAX_RR @SPE100
Thr 0.519 0.619 0.465 0.623 7.56e-01
RR 3.806 3.548 4.160 5.069 3.91e+01
RR_LCI 2.082 1.642 2.391 1.954 8.17e-02
RR_UCI 6.957 7.666 7.237 13.150 1.87e+04
SEN 0.901 0.941 0.881 0.960 1.00e+00
SPE 0.397 0.247 0.485 0.242 5.67e-02
BACC 0.649 0.594 0.683 0.601 5.28e-01 
pander::pander(RRAnalysisCI$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.698 0.698 0.65 0.743 
pander::pander(t(RRAnalysisCI$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.692 0.631 0.752 
pander::pander((RRAnalysisCI$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.891 0.813 0.944 
pander::pander((RRAnalysisCI$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.397 0.328 0.469 
pander::pander(t(RRAnalysisCI$thr_atP),caption="Probability Thresholds")
Probability Thresholds
10% 5%
0.517 0.618 
pander::pander(RRAnalysisCI$surdif,caption="Logrank test")
Logrank test Chisq = 28.085735 on 2 degrees of freedom, p = 0.000001
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 55 6 23.5 13.01 17.1
class=1 33 5 12.9 4.87 5.6
class=2 207 90 64.6 10.00 27.9

Node positive data

RR Plot Signature correlation

NodePdata <- subset(pdata,Posnodes=="y")

rdata <- cbind(NodePdata$TTMevent,NodePdata$C1used)


RRAnalysisPos <- RRPlot(rdata,atRate=c(0.90,0.95),
                     timetoEvent=NodePdata$RFS,
                     title="Signature: Breast Cancer",
                     ysurvlim=c(0.00,1.0))

par(op)

CI Performance positive data

pander::pander(t(RRAnalysisPos$keyPoints),caption="Threshold values")
Threshold values
  @:0.9 @:0.95 @MAX_BACC @MAX_RR @SPE100
Thr 0.486 0.655 0.267 0.486 7.17e-01
RR 3.231 1.579 3.083 3.231 1.34e+01
RR_LCI 1.377 0.563 1.746 1.377 2.94e-02
RR_UCI 7.578 4.431 5.444 7.578 6.14e+03
SEN 0.894 0.936 0.745 0.894 1.00e+00
SPE 0.361 0.113 0.639 0.361 4.12e-02
BACC 0.627 0.525 0.692 0.627 5.21e-01 
pander::pander(RRAnalysisPos$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.7 0.7 0.63 0.767 
pander::pander(t(RRAnalysisPos$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.669 0.576 0.761 
pander::pander((RRAnalysisPos$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.894 0.769 0.965 
pander::pander((RRAnalysisPos$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.371 0.275 0.475 
pander::pander(t(RRAnalysisPos$thr_atP),caption="Probability Thresholds")
Probability Thresholds
10% 5%
0.484 0.651 
pander::pander(RRAnalysisPos$surdif,caption="Logrank test")
Logrank test Chisq = 11.060876 on 2 degrees of freedom, p = 0.003964
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 15 3 5.80 1.35 1.55
class=1 26 2 9.73 6.14 7.77
class=2 103 42 31.47 3.52 10.71

Node Negative data

RR Plot Signature correlation

NodeNdata <- subset(pdata,Posnodes=="n")

rdata <- cbind(NodeNdata$TTMevent,NodeNdata$C1used)


RRAnalysisNeg <- RRPlot(rdata,atRate=c(0.90,0.95),
                     timetoEvent=NodeNdata$RFS,
                     title="Signature: Breast Cancer",
                     ysurvlim=c(0.00,1.0))

par(op)

CI Performance negative data

pander::pander(t(RRAnalysisNeg$keyPoints),caption="Threshold values")
Threshold values
  @:0.9 @:0.95 @MAX_BACC @MAX_RR @SPE100
Thr 0.507 0.585 0.465 0.623 7.56e-01
RR 4.454 5.920 5.130 15.402 3.42e+01
RR_LCI 2.040 1.959 2.344 2.211 7.18e-02
RR_UCI 9.723 17.889 11.228 107.305 1.63e+04
SEN 0.889 0.944 0.889 0.981 1.00e+00
SPE 0.495 0.371 0.546 0.340 9.28e-02
BACC 0.692 0.658 0.718 0.661 5.46e-01 
pander::pander(RRAnalysisNeg$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.695 0.696 0.63 0.764 
pander::pander(t(RRAnalysisNeg$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.708 0.626 0.79 
pander::pander((RRAnalysisNeg$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.889 0.774 0.958 
pander::pander((RRAnalysisNeg$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.495 0.392 0.598 
pander::pander(t(RRAnalysisNeg$thr_atP),caption="Probability Thresholds")
Probability Thresholds
10% 5%
0.513 0.583 
pander::pander(RRAnalysisNeg$surdif,caption="Logrank test")
Logrank test Chisq = 24.223875 on 2 degrees of freedom, p = 0.000005
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 40 3 18.18 12.67 19.29
class=1 14 3 5.43 1.09 1.21
class=2 97 48 30.39 10.21 23.58

RRPlot Cox Model

timeinterval <- 5 # Five years

h0 <- sum(pdata$TTMevent & pdata$RFS <= timeinterval)
h0 <- h0/sum((pdata$RFS > timeinterval) | (pdata$TTMevent==1))

mcox <- coxph(Surv(RFS,TTMevent)~C1used,pdata)
pander::pander(summary(mcox)$coefficients)
  coef exp(coef) se(coef) z Pr(>|z|)
C1used -1.5 0.224 0.263 -5.69 1.3e-08 
index <- predict(mcox,pdata)
rdata <- cbind(pdata$TTMevent,ppoisGzero(index,h0))


RRAnalysisCox <- RRPlot(rdata,atRate=c(0.90,0.95),
                     timetoEvent=pdata$RFS,
                     title="NIK: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

par(op)

By Risk Categories

obsexp <- RRAnalysisCox$OERatio$atThrEstimates
pander::pander(obsexp)
  Observed L.CI H.CI Expected pvalue
Total 101 82.27 122.7 125.3 0.0285
low 6 2.20 13.1 14.7 0.0181
10% 5 1.62 11.7 9.4 0.1893
5% 90 72.37 110.6 99.0 0.3928 
maxx <- 1.1*max(c(obsexp$Observed,obsexp$Expected))
minx <- 0.9*min(c(obsexp$Observed,obsexp$Expected))

plot(obsexp$Expected,obsexp$Observed,
     xlim=c(minx,maxx),
     ylim=c(minx,maxx),
     main="Expected vs Observed",
     ylab="Observed",
     xlab="Expected",
     col=rainbow(nrow(obsexp)),
     log="xy")

errbar(obsexp$Expected,obsexp$Observed,obsexp$L.CI,obsexp$H.CI,add=TRUE,pch=0,errbar.col=rainbow(nrow(obsexp)),cex=0.75)
lines(x=c(1,maxx),y=c(1,maxx),lty=2)
text(obsexp$Expected,obsexp$Observed,rownames(obsexp),pos=2,cex=0.75)

Unadjusted Cox Performance

pander::pander(t(RRAnalysisCox$keyPoints),caption="Threshold values")
Threshold values
  @:0.9 @:0.95 @MAX_BACC @MAX_RR @SPE100 p(0.5)
Thr 0.176 0.154 0.190 0.153 1.27e-01 0.5041
RR 3.806 3.548 4.160 5.069 3.91e+01 0.9241
RR_LCI 2.082 1.642 2.391 1.954 8.17e-02 0.4906
RR_UCI 6.957 7.666 7.237 13.150 1.87e+04 1.7407
SEN 0.901 0.941 0.881 0.960 1.00e+00 0.0693
SPE 0.397 0.247 0.485 0.242 5.67e-02 0.9227
BACC 0.649 0.594 0.683 0.601 5.28e-01 0.4960
NetBenefit 0.223 0.232 0.222 0.239 2.52e-01 -0.0279 
pander::pander(t(RRAnalysisCox$OERatio$estimate),caption="O/E Ratio")
O/E Ratio
O/E Low Upper p.value
0.806 0.656 0.979 0.0285 
pander::pander(t(RRAnalysisCox$OE95ci),caption="O/E Mean")
O/E Mean
mean 50% 2.5% 97.5%
0.952 0.953 0.926 0.979 
pander::pander(t(RRAnalysisCox$OAcum95ci),caption="O/Acum Mean")
O/Acum Mean
mean 50% 2.5% 97.5%
1.15 1.15 1.14 1.17 
pander::pander(RRAnalysisCox$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.698 0.698 0.649 0.744 
pander::pander(t(RRAnalysisCox$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.692 0.631 0.752 
pander::pander((RRAnalysisCox$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.891 0.813 0.944 
pander::pander((RRAnalysisCox$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.397 0.328 0.469 
pander::pander(t(RRAnalysisCox$thr_atP),caption="Probability Thresholds")
Probability Thresholds
10% 5%
0.177 0.154 
pander::pander(RRAnalysisCox$surdif,caption="Logrank test")
Logrank test Chisq = 28.085735 on 2 degrees of freedom, p = 0.000001
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 55 6 23.5 13.01 17.1
class=1 33 5 12.9 4.87 5.6
class=2 207 90 64.6 10.00 27.9

RRPlot Cox Adjusted Model

This time we will include Lymph node status from pathology report and Estrogen receptor alpha expression measurement from microarray

mcox <- coxph(Surv(RFS,TTMevent)~C1used*(ESR1 + Posnodes),pdata)
pander::pander(summary(mcox)$coefficients)
  coef exp(coef) se(coef) z Pr(>|z|)
C1used -0.403 0.668 0.629 -0.640 0.52186
ESR1 0.123 1.131 0.255 0.481 0.63079
Posnodesy -0.305 0.737 0.217 -1.401 0.16112
C1used:ESR1 -1.913 0.148 0.739 -2.588 0.00966
C1used:Posnodesy 0.378 1.460 0.583 0.649 0.51661 
index <- predict(mcox,pdata)
rdata <- cbind(pdata$TTMevent,ppoisGzero(index,h0))


RRAnalysisAdCox <- RRPlot(rdata,atRate=c(0.90,0.95),
                     timetoEvent=pdata$RFS,
                     title="Adjusted: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

par(op)

By Risk Categories

obsexp <- RRAnalysisAdCox$OERatio$atThrEstimates
pander::pander(obsexp)
  Observed L.CI H.CI Expected pvalue
Total 101 82.27 122.7 122.43 0.0519
low 6 2.20 13.1 12.68 0.0658
10% 5 1.62 11.7 7.37 0.5762
5% 90 72.37 110.6 100.46 0.3183 
maxx <- 1.1*max(c(obsexp$Observed,obsexp$Expected))
minx <- 0.9*min(c(obsexp$Observed,obsexp$Expected))

plot(obsexp$Expected,obsexp$Observed,
     xlim=c(minx,maxx),
     ylim=c(minx,maxx),
     main="Ad. Expected vs Observed",
     ylab="Observed",
     xlab="Expected",
     col=rainbow(nrow(obsexp)),
     log="xy")

errbar(obsexp$Expected,obsexp$Observed,obsexp$L.CI,obsexp$H.CI,add=TRUE,pch=0,errbar.col=rainbow(nrow(obsexp)),cex=0.75)
lines(x=c(1,maxx),y=c(1,maxx),lty=2)
text(obsexp$Expected,obsexp$Observed,rownames(obsexp),pos=2,cex=0.75)

Adjusted Cox Performance

pander::pander(t(RRAnalysisAdCox$keyPoints),caption="Threshold values")
Threshold values
  @:0.9 @:0.95 @MAX_BACC @MAX_RR @SPE100 p(0.5)
Thr 0.159 0.133 0.205 0.133 9.92e-02 0.50740
RR 3.422 4.043 3.235 4.699 3.54e+01 1.72657
RR_LCI 1.928 1.863 2.100 2.004 7.42e-02 1.06501
RR_UCI 6.075 8.773 4.984 11.015 1.69e+04 2.79908
SEN 0.891 0.941 0.802 0.950 1.00e+00 0.07921
SPE 0.392 0.278 0.572 0.273 5.15e-02 0.96907
BACC 0.641 0.609 0.687 0.612 5.26e-01 0.52414
NetBenefit 0.230 0.249 0.202 0.252 2.74e-01 0.00617 
pander::pander(t(RRAnalysisAdCox$OERatio$estimate),caption="O/E Ratio")
O/E Ratio
O/E Low Upper p.value
0.825 0.672 1 0.0519 
pander::pander(t(RRAnalysisAdCox$OE95ci),caption="O/E Mean")
O/E Mean
mean 50% 2.5% 97.5%
0.973 0.975 0.947 0.999 
pander::pander(t(RRAnalysisAdCox$OAcum95ci),caption="O/Acum Mean")
O/Acum Mean
mean 50% 2.5% 97.5%
1.18 1.18 1.17 1.19 
pander::pander(RRAnalysisAdCox$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.707 0.706 0.658 0.75 
pander::pander(t(RRAnalysisAdCox$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.702 0.642 0.763 
pander::pander((RRAnalysisAdCox$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.891 0.813 0.944 
pander::pander((RRAnalysisAdCox$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.397 0.328 0.469 
pander::pander(t(RRAnalysisAdCox$thr_atP),caption="Probability Thresholds")
Probability Thresholds
10% 5%
0.159 0.133 
pander::pander(RRAnalysisAdCox$surdif,caption="Logrank test")
Logrank test Chisq = 28.504862 on 2 degrees of freedom, p = 0.000001
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 60 6 25.3 14.73 19.76
class=1 28 5 11.2 3.45 3.89
class=2 207 90 64.5 10.11 28.16

Calibrating the index

calprob <- CoxRiskCalibration(mcox,pdata,"TTMevent","RFS")

( 7.470999 , 626.7032 , 1.025293 , 101 , 118.8774 )

pander::pander(c(h0=calprob$h0,
                 Gain=calprob$hazardGain,
                 DeltaTime=calprob$timeInterval),
               caption="Cox Calibration Parameters")
h0 Gain DeltaTime
0.421 1.04 7.47 
h0 <- calprob$h0
timeinterval <- calprob$timeInterval;

rdata <- cbind(pdata$TTMevent,calprob$prob)


RRAnalysisCalAdCox <- RRPlot(rdata,atRate=c(0.80,0.90),
                     timetoEvent=pdata$RFS,
                     title="Cal. NIK: Breast Cancer",
                     ysurvlim=c(0.00,1.0),
                     riskTimeInterval=timeinterval)

par(op)

By Risk Categories

obsexp <- RRAnalysisCalAdCox$OERatio$atThrEstimates
pander::pander(obsexp)
  Observed L.CI H.CI Expected pvalue
Total 101 82.27 122.7 120.1 0.0829
low 11 5.49 19.7 19.7 0.0539
20% 10 4.80 18.4 13.6 0.4145
10% 80 63.44 99.6 84.9 0.6639 
maxx <- 1.1*max(c(obsexp$Observed,obsexp$Expected))
minx <- 0.9*min(c(obsexp$Observed,obsexp$Expected))

plot(obsexp$Expected,obsexp$Observed,
     xlim=c(minx,maxx),
     ylim=c(minx,maxx),
     main="Cal. Expected vs Observed",
     ylab="Observed",
     xlab="Expected",
     col=rainbow(nrow(obsexp)),
     log="xy")

errbar(obsexp$Expected,obsexp$Observed,obsexp$L.CI,obsexp$H.CI,add=TRUE,pch=0,errbar.col=rainbow(nrow(obsexp)),cex=0.75)
lines(x=c(1,maxx),y=c(1,maxx),lty=2)
text(obsexp$Expected,obsexp$Observed,rownames(obsexp),pos=2,cex=0.75)

Calibrated and Adjusted Cox Performance

pander::pander(t(RRAnalysisCalAdCox$keyPoints),caption="Threshold values")
Threshold values
  @:0.8 @:0.9 @MAX_BACC @MAX_RR @SPE100 p(0.5)
Thr 0.285 0.224 0.285 0.188 1.42e-01 0.4924
RR 3.235 3.422 3.235 4.699 3.54e+01 1.8140
RR_LCI 2.100 1.928 2.100 2.004 7.42e-02 1.3369
RR_UCI 4.984 6.075 4.984 11.015 1.69e+04 2.4614
SEN 0.802 0.891 0.802 0.950 1.00e+00 0.3564
SPE 0.572 0.392 0.572 0.273 5.15e-02 0.8299
BACC 0.687 0.641 0.687 0.612 5.26e-01 0.5932
NetBenefit 0.162 0.190 0.162 0.215 2.39e-01 0.0135 
pander::pander(t(RRAnalysisCalAdCox$OERatio$estimate),caption="O/E Ratio")
O/E Ratio
O/E Low Upper p.value
0.841 0.685 1.02 0.0829 
pander::pander(t(RRAnalysisCalAdCox$OE95ci),caption="O/E Mean")
O/E Mean
mean 50% 2.5% 97.5%
0.992 0.992 0.961 1.02 
pander::pander(t(RRAnalysisCalAdCox$OAcum95ci),caption="O/Acum Mean")
O/Acum Mean
mean 50% 2.5% 97.5%
1 1 0.995 1.01 
pander::pander(RRAnalysisCalAdCox$c.index$cstatCI,caption="C. Index")
mean.C Index median lower upper
0.707 0.707 0.664 0.749 
pander::pander(t(RRAnalysisCalAdCox$ROCAnalysis$aucs),caption="ROC AUC")
ROC AUC
est lower upper
0.702 0.642 0.763 
pander::pander((RRAnalysisCalAdCox$ROCAnalysis$sensitivity),caption="Sensitivity")
Sensitivity
est lower upper
0.792 0.7 0.866 
pander::pander((RRAnalysisCalAdCox$ROCAnalysis$specificity),caption="Specificity")
Specificity
est lower upper
0.572 0.499 0.643 
pander::pander(t(RRAnalysisCalAdCox$thr_atP),caption="Probability Thresholds")
Probability Thresholds
20% 10%
0.286 0.224 
pander::pander(RRAnalysisCalAdCox$surdif,caption="Logrank test")
Logrank test Chisq = 43.461969 on 2 degrees of freedom, p = 0.000000
  N Observed Expected (O-E)^2/E (O-E)^2/V
class=0 88 11 36.5 17.85 28.16
class=1 44 10 17.0 2.88 3.47
class=2 163 80 47.5 22.30 42.48

Comparing Risks

Comparing concordance Index

## Correlation Index
cindex <- RRAnalysisCI$c.index$cstatCI
## Cox Index
cindex <- rbind(cindex,RRAnalysisCox$c.index$cstatCI)
## Adjusted Cox Index
cindex <- rbind(cindex,RRAnalysisAdCox$c.index$cstatCI)
## Adjusted and Calibrated Cox Index
cindex <- rbind(cindex,RRAnalysisCalAdCox$c.index$cstatCI)
rownames(cindex) <- c("CI","Cox","Adj. Cox","Cal. Adj. Cox")

pander::pander(cindex)
  mean.C Index median lower upper
CI 0.698 0.698 0.650 0.743
Cox 0.698 0.698 0.649 0.744
Adj. Cox 0.707 0.706 0.658 0.750
Cal. Adj. Cox 0.707 0.707 0.664 0.749

Comparing Risk Ratios Index

## Correlation Index
RRratio <- c(RR=RRAnalysisCI$keyPoints$RR[1],
             LCI=RRAnalysisCI$keyPoints$RR_LCI[1],
             UCI=RRAnalysisCI$keyPoints$RR_UCI[1])
## Cox Index
RRratio <- rbind(RRratio,c(RR=RRAnalysisCox$keyPoints$RR[1],
                           LCI=RRAnalysisCox$keyPoints$RR_LCI[1],
                           UCI=RRAnalysisCox$keyPoints$RR_UCI[1]))
## Adjusted Cox Index
RRratio <- rbind(RRratio,c(RR=RRAnalysisAdCox$keyPoints$RR[1],
                           LCI=RRAnalysisAdCox$keyPoints$RR_LCI[1],
                           UCI=RRAnalysisAdCox$keyPoints$RR_UCI[1]))
## Adjusted and Calibrated Cox Index
RRratio <- rbind(RRratio,c(RR=RRAnalysisCalAdCox$keyPoints$RR[1],
                           LCI=RRAnalysisCalAdCox$keyPoints$RR_LCI[1],
                           UCI=RRAnalysisCalAdCox$keyPoints$RR_UCI[1]))
rownames(RRratio) <- c("CI","Cox","Adj. Cox","Cal. Adj. Cox")
pander::pander(RRratio)
  RR LCI UCI
CI 3.81 2.08 6.96
Cox 3.81 2.08 6.96
Adj. Cox 3.42 1.93 6.07
Cal. Adj. Cox 3.24 2.10 4.98

Comparing logRank values

## Correlation Index
SurvDif <- c(chisq=RRAnalysisCI$surdif$chisq,pvalue=RRAnalysisCI$surdif$pvalue)
## Cox Index
SurvDif <- rbind(SurvDif,c(chisq=RRAnalysisCox$surdif$chisq,pvalue=RRAnalysisCox$surdif$pvalue))
## Adjusted Cox Index
SurvDif <- rbind(SurvDif,c(chisq=RRAnalysisAdCox$surdif$chisq,pvalue=RRAnalysisAdCox$surdif$pvalue))
## Adjusted and Calibrated Cox Index
SurvDif <- rbind(SurvDif,c(chisq=RRAnalysisCalAdCox$surdif$chisq,pvalue=RRAnalysisCalAdCox$surdif$pvalue))
rownames(SurvDif) <- c("CI","Cox","Adj. Cox","Cal. Adj. Cox")

pander::pander(SurvDif)
  chisq pvalue
CI 28.1 7.97e-07
Cox 28.1 7.97e-07
Adj. Cox 28.5 6.46e-07
Cal. Adj. Cox 43.5 3.65e-10

Comparing Sensitivity

## Correlation Index
sensi <- RRAnalysisCI$ROCAnalysis$sensitivity
## Cox Index
sensi <- rbind(sensi,RRAnalysisCox$ROCAnalysis$sensitivity)
## Adjusted Cox Index
sensi <- rbind(sensi,RRAnalysisAdCox$ROCAnalysis$sensitivity)
## Adjusted and Calibrated Cox Index
sensi <- rbind(sensi,RRAnalysisCalAdCox$ROCAnalysis$sensitivity)
rownames(sensi) <- c("CI","Cox","Adj. Cox","Cal. Adj. Cox")

pander::pander(sensi)
  est lower upper
CI 0.891 0.813 0.944
Cox 0.891 0.813 0.944
Adj. Cox 0.891 0.813 0.944
Cal. Adj. Cox 0.792 0.700 0.866

Comparing Specificity

## Correlation Index
speci <- RRAnalysisCI$ROCAnalysis$specificity
## Cox Index
speci <- rbind(speci,RRAnalysisCox$ROCAnalysis$specificity)
## Adjusted Cox Index
speci <- rbind(speci,RRAnalysisAdCox$ROCAnalysis$specificity)
## Adjusted and Calibrated Cox Index
speci <- rbind(speci,RRAnalysisCalAdCox$ROCAnalysis$specificity)
rownames(speci) <- c("CI","Cox","Adj. Cox","Cal. Adj. Cox")
pander::pander(speci)
  est lower upper
CI 0.397 0.328 0.469
Cox 0.397 0.328 0.469
Adj. Cox 0.397 0.328 0.469
Cal. Adj. Cox 0.572 0.499 0.643

Comparing O/E

OERatio <- NULL
## Cox Index
OERatio <- rbind(OERatio,RRAnalysisCox$OERatio$estimate)
## Adjusted Cox Index
OERatio <- rbind(OERatio,RRAnalysisAdCox$OERatio$estimate)
## Adjusted and Calibrated Cox Index
OERatio <- rbind(OERatio,RRAnalysisCalAdCox$OERatio$estimate)
rownames(OERatio) <- c("Cox","Adj. Cox","Cal. Adj. Cox")

pander::pander(OERatio)
  O/E Low Upper p.value
Cox 0.806 0.656 0.979 0.0285
Adj. Cox 0.825 0.672 1.002 0.0519
Cal. Adj. Cox 0.841 0.685 1.022 0.0829

Comparing O/Acum

OARatio <- NULL
## Cox Index
OARatio <- rbind(OARatio,RRAnalysisCox$OARatio$estimate)
## Adjusted Cox Index
OARatio <- rbind(OARatio,RRAnalysisAdCox$OARatio$estimate)
## Adjusted and Calibrated Cox Index
OARatio <- rbind(OARatio,RRAnalysisCalAdCox$OARatio$estimate)
rownames(OARatio) <- c("Cox","Adj. Cox","Cal. Adj. Cox")
pander::pander(OARatio)
  O/A Low Upper p.value
Cox 1.15 0.936 1.40 0.165
Adj. Cox 1.18 0.961 1.43 0.104
Cal. Adj. Cox 1.01 0.823 1.23 0.881

Comparing NetBenefit

NetBen <- NULL
## Cox Index
NetBen <- rbind(NetBen,RRAnalysisCox$keyPoints$NetBenefit)
## Adjusted Cox Index
NetBen <- rbind(NetBen,RRAnalysisAdCox$keyPoints$NetBenefit)
## Adjusted and Calibrated Cox Index
NetBen <- rbind(NetBen,RRAnalysisCalAdCox$keyPoints$NetBenefit)
colnames(NetBen) <- rownames(RRAnalysisCox$keyPoints)
rownames(NetBen) <- c("Cox","Adj. Cox","Cal. Adj. Cox")
pander::pander(NetBen)
  @:0.9 @:0.95 @MAX_BACC @MAX_RR @SPE100 p(0.5)
Cox 0.223 0.232 0.222 0.239 0.252 -0.02795
Adj. Cox 0.230 0.249 0.202 0.252 0.274 0.00617
Cal. Adj. Cox 0.162 0.190 0.162 0.215 0.239 0.01354

Compare the ROC AUC

pander::pander(pROC::roc.test(RRAnalysisCI$ROCAnalysis$ROC.analysis$roc.predictor,
                              RRAnalysisAdCox$ROCAnalysis$ROC.analysis$roc.predictor))
DeLong’s test for two correlated ROC curves: RRAnalysisCI$ROCAnalysis$ROC.analysis$roc.predictor and RRAnalysisAdCox$ROCAnalysis$ROC.analysis$roc.predictor
Test statistic P value Alternative hypothesis AUC of roc1 AUC of roc2
-0.993 0.321 two.sided 0.692 0.702